But most interpretations have the same statistical predictions as standard QM. The standard Copenhagen setup can be argued to not actually be a theory (the split between quantum and classical in a fundamental theory is an absurdity since the classical is made up of quantum ), but assuming that an interpretation is clear enough to be called a theory and has the same statistical framework as standard quantum mechanics, then experiments will not distinguish them.

The different interpretations, however, may lead to different insights for extending the theory. And in that game, one may pull ahead of the other. For example PWT inspired Bell's results. PWT can also explain the impact of the topology of configuration space convincingly since the configuration is a fundamental part of the theory. It leads to many insights that the others just have to assume.

GRW with a flash ontology has a relativistic version with no foliations. So that's cool.